Handling editor: Hinke Osinga

BRIDGES LEEUWARDEN

Mathematics, Music, Art, Architecture, Culture

by Bernd Krauskopf, University of Bristol

The annual Bridges conference is one of the leading conferences in Mathematics and the Arts with the goal of exploring ``Mathematical Connections in Art, Music, and Science.'' While Bridges has a large and dedicated following, it may not be known so well beyond the `in-crowd' of regular attendees. In fact, I only heard of it very indirectly about three-years ago, via a colleague in Montreal, and attended for the first time when it was held in London in 2006.

Leeuwarden's leaning tower Oldehove.		M.C. Escher was born close to the Oldehove in the Princessehof in 1898.

This July Bridges 2008 took place in the city of Leeuwarden, the Netherlands. This splendid town is the capital of the Dutch province of Frisia, or Fryslân in the local Frisian language (which happens to be the language closest to English), which is generally known as the region where the black and white cows come from. But it is probably less well known that Leeuwarden is the birthplace of artist M.C. Escher, who was born there 110 years ago. This fact was the direct reason for the choice of location, and Escher's work was celebrated in many different ways. A real highlight was an exhibition of originals of some of his most famous prints. What a treat to be allowed to scrutinize the incredible mathematical and technical craftsmanship of classics such as Belvedere and Circle Limit III.

Fractal artwork by Mehrdad Garousi; from Bridges 2008 Gallery.

The atmosphere at Bridges 2008 was quite special: it felt like a mathematical holiday camp! People from all over the world and with all kinds of backgrounds came together for this meeting, driven by a passion for mathematical arts. The programme was very varied, as is evidenced by the conference proceedings of more than 450 pages. There truly was something to discover for everyone: from abstract mathematics, such as Kleinian groups and tesselations of space, via all kinds of mathematical puzzles and toys to artwork including painting, paper art and sculpture. Apart from a stimulating series of plenary and contributed talks, there were several events that are Bridges traditions. An exhibition of mathematical art by participants served as the heart of the conference and a natural meeting place. The last day of the conference was as always a Family Day, effectively a mathematical street fair in the center of Leeuwarden. A real highlight was the excursion: a bus tour to seven small churches in villages around Leeuwarden, each featuring an exhibition of work by a different artist. The organizing committee, and especially local organizer Cor Wetting of The City of Leeuwarden/The Foundation Passages, really did an exceptional job; even the weather was great.

Fractal puzzles by Edmund Harris in their natural environment; from Bridges 2008 Gallery.

But what does all this have to do with dynamical systems? I think a lot, and I will give three specific examples. You will have seen art of a fractal nature, generated by a dynamical system of one sort or another. But did you know that it is possible to construct fractal puzzles with self-similar pieces by considering Markov partitions of hyperbolic automorphisms of the 4-torus? Edmund Harris has done just that: participants could play with his beautiful lasercut wooden puzzles. Another example is the work by artist/writer/creative developer Paul Prudence, who takes video feedback to a new and artistic level via software-based recursion methods. His video installations are truly dynamic and react to the environment, for example, to musical input. A more practical example is the work of Erik Moncrieff, who has been developing mathematical and computer tools for the design of doubly curved architectural structures. This involves, for example, determining dynamic wind loads on tent-like roofs. If this does not mean much to you, his software was used for many of the spectacular architectural structures at the Beijing Olympics!

A still from Paul Prudence's real-time generative video feedback system Talysis 2; from http://www.transphormetic.com/.

I could go on, but the best is to take a relaxing tour of mathematical art at the online Mathematical Art Exhibits and to check out the Bridges Proceedings available at mathartfun.com. Another great resource (officially launched at Bridges 2006) is the Journal of Mathematics and the Arts. And if you really catch the bug, the next Bridges conference will take place at Banff Research Station in July 2009.